Hacker: A hacker denotes a skilled computer expert that uses technical knowledge to overcome a problem. The bugs or exploits are been used by hacker to break into computer systems. The hacker is able to subvert computer security . It mostly denotes computer criminals due to unethical tasks performed. It can be stated as a person who messes about with something with positive sense. Phishing attack: It denotes a fraudulent e-mail sent to retrieve personal data from recipient It is more or less random. The malware may get downloaded to device. It may redirect into fake website to retrieve personal information. The information may be sold in black market for money. Spear phishing attack: The fraudulent e-mails are sent to employee of an organization. The attack is more precise and narrow. The malware may get installed into particular device. It may be targeted to get sensitive company information or voucher money. The task may be targeted to provide harm to a particular organization.

Question

Design a dynamic programming algorithm for the Longest Alternating Subsequence problem described below: Input: A sequence of n integers Output: The length of the longest subsequence where the numbers alternate between being larger and smaller than their predecessor The algorithm must take O(n²) time. You must also write and explain the recurrence. Example 1: Input: [3, 5, 4, 1, 3, 6, 5, 7, 3, 4] Output: 8 ([3, 5, 4, 6, 5, 7, 3, 4]) Example 2: Input: [4,7,2,5,8, 3, 8, 0, 4, 7, 8] Output: 8 ([4, 7, 2, 5, 3, 8, 0,4]) (Take your time with this for the subproblem for this one)

Answer 1

Question

Chapter 13, Problem 4DQ

Program Plan Intro

Hacker:

A hacker denotes a skilled computer expert that uses technical knowledge to overcome a problem.

The bugs or exploits are been used by hacker to break into computer systems.

The hacker is able to subvert computer security.

It mostly denotes computer criminals due to unethical tasks performed.

It can be stated as a person who messes about with something with positive sense.

Phishing attack:

It denotes a fraudulent e-mail sent to retrieve personal data from recipient

It is more or less random.

The malware may get downloaded to device.

It may redirect into fake website to retrieve personal information.

The information may be sold in black market for money.

Spear phishing attack:

The fraudulent e-mails are sent to employee of an organization.

The attack is more precise and narrow.

The malware may get installed into particular device.

It may be targeted to get sensitive company information or voucher money.

The task may be targeted to provide harm to a particular organization.

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Design a dynamic programming algorithm for the Longest Alternating Subsequence problem described below: Input: A sequence of n integers Output: The length of the longest subsequence where the numbers alternate between being larger and smaller than their predecessor The algorithm must take O(n²) time. You must also write and explain the recurrence. Example 1: Input: [3, 5, 4, 1, 3, 6, 5, 7, 3, 4] Output: 8 ([3, 5, 4, 6, 5, 7, 3, 4]) Example 2: Input: [4,7,2,5,8, 3, 8, 0, 4, 7, 8] Output: 8 ([4, 7, 2, 5, 3, 8, 0,4]) (Take your time with this for the subproblem for this one)

Design a dynamic programming algorithm for the Coin-change problem described below: Input: An amount of money C and a set of n possible coin values with an unlimited supply of each kind of coin. Output: The smallest number of coins that add up to C exactly, or output that no such set exists. The algorithm must take O(n C) time. You must also write and explain the recurrence. Example 1: Input: C24, Coin values = = [1, 5, 10, 25, 50] Output: 6 (since 24 = 10+ 10+1+1 +1 + 1) Example 2: Input: C = 86, Coin values = [1, 5, 6, 23, 35, 46, 50] Output: 2 (since 86 = 46+35+5)

Design a dynamic programming algorithm for the Longest Common Subsequence problem de- scribed below Input: Two strings x = x1x2 xm and y = Y1Y2... Yn Output: The length of the longest subsequence that is common to both x and y. . The algorithm must take O(m n) time. You must also write and explain the recurrence. (I want the largest k such that there are 1 ≤ i₁ < ... < ik ≤ m and 1 ≤ j₁ < ... < jk ≤ n such that Xi₁ Xi2 Xik = Yj1Yj2 ··· Yjk) Example 1: Input: x = 'abcdefghijklmnopqrst' and y = 'ygrhnodsh ftw' Output: 6 ('ghnost' is the longest common subsequence to both strings) Example 2: Input: x = 'ahshku' and y = ‘asu' Output: 3 ('asu' is the longest common subsequence to both strings)